Monetary Policy and the Predictability of Nominal Exchange Rates Martin Eichenbaum Ben Johannsen Sergio Rebelo Disclaimer: The views expressed here are those of the authors and do not necessarily reflect the views of the Federal Reserve Board, the FOMC, or anyone else associated with the Federal Reserve System.
Introduction Two facts about countries with floating exchange rates where monetary policy follows a Taylor-type rule: 1. RER is highly negatively correlated with future changes in NER at horizons greater than two years. Correlation is stronger the longer is the horizon. 2. RER is virtually uncorrelated with future inflation rates at all horizons. Relative PPP is re-established via changes in the NER, not via changes in prices. When a country s consumption basket is relatively expensive, its NER eventually depreciates by enough to move the RER back to its long-run level
Introduction Redo our analysis for China which is on a quasi-fixed exchange rate regime versus the U.S. dollar, Hong Kong which has a fixed exchange rate versus the U.S. dollar, Euro area countries which have fixed exchange rates with each other. Current RER is highly correlated with future relative inflation rates. RER adjusts overwhelmingly through prices.
Introduction We develop two-country models that can account for our observations about flexible exchange rate regimes. Key model features: Taylor rules for monetary policy. Home bias in consumption.
Introduction Our results hold whether Prices are flexible or sticky; Markets are complete or incomplete; Internal persistence from habit formation and interest-rate smoothing, or not; Capital is an input to production, or not. Results also hold in presence of interest rate spread shocks which invalidate UIP. Use sequence of models to develop intuition about key mechanisms underlying our explanation of the facts.
Introduction Is our proposed explanation consistent with other features of the data stressed in literature? RER and NER co-move closely in the short run (Mussa (1986)). RERs are highly inertial (Rogoff (1996)). Conventional tests reject UIP. We show that a medium-size DSGE version of our model with nominal rigidities is consistent with those features of the data, and the quantitative relationship between current RER and future changes in inflation and the NER. Sequel to paper: out-of-sample forecasting properties of our model.
NER regression Define the RER as: RER t = NER tp t P t P t = home consumer price index; P t = foreign consumer price index. A rise in the NER corresponds to a depreciation of the $ and an appreciation of the FCU. NER regression ( ) NER t+j log NER t = β NER 0,j + β NER 1,j log (RER t ) + ɛ t,t+j.
Canada RER t 0.0 log(rer t ) 0.1 0.2 0.3 0.4 1980 1990 2000 2010 Date Rise in RER is a rise in price of Canadian consumption basket in units of the U.S. consumption basket.
NER regression data: Canada 0.25 0.00 0.25 0.50 0.2 0.1 0.0 0.1 0.2 log(rer t ) log(ner t+j NER t ) 1 year horizon
NER regression data: Canada 0.25 0.00 0.25 0.50 0.2 0.1 0.0 0.1 0.2 log(rer t ) log(ner t+j NER t ) 3 year horizon
NER regression data: Canada 0.25 0.00 0.25 0.50 0.2 0.1 0.0 0.1 0.2 log(rer t ) log(ner t+j NER t ) 5 year horizon
NER regression data: Canada 7 year horizon 0.50 log(ner t+j NER t ) 0.25 0.00 0.25 0.2 0.1 0.0 0.1 0.2 log(rer t )
NER regression data: Canada 10 year horizon 0.50 log(ner t+j NER t ) 0.25 0.00 0.25 0.2 0.1 0.0 0.1 0.2 log(rer t )
NER regression results: Canada ( ) NER t+j log NER t = β NER 0,j + β NER 1,j log (RER t ) + ɛ t,t+j. Horizon (in years) 1 3 5 7 10 ˆβ 1,j NER -0.122-0.549-0.944-1.158-1.661 (0.073) (0.184) (0.186) (0.143) (0.123) R 2 0.078 0.349 0.590 0.687 0.878 A high Cdn RER is associated with future depreciations of the Cdn dollar.
Rel.-price regression results: Canada Quantify NER change from relative price changes ( P t+j /P ) t log = β0,j π + β1,j π log (RER t ) + ɛ t,t+j. P t+j /P t Horizon (in years) 1 3 5 7 10 ˆβ 1,j π 0.014 0.033 0.040 0.075 0.258 (0.015) (0.044) (0.064) (0.106) (0.183) R 2 0.011 0.016 0.014 0.024 0.102 A high Cdn RER is not associated with changes in future relative inflation rates.
Regression results: China and France Consider our NER regression ( ) NER t+j log = β0,j NER + β1,j NER log (RER t ) + ɛ t,t+j. NER t for China vis-à-vis US$ and France vis-à-vis Germany. China France Horizon (in years) 1 3 5 NER ˆβ 1,j -0.123-0.208-0.261 (0.035) (0.060) (0.096) ˆβ NER 1,j 0.000 0.000 0.000
Regression results: China and France Relative-price regression ( P t+j /P ) t log = β0,j π + β1,j π log (RER t ) + ɛ t,t+j. P t+j /P t Horizon (in years) 1 3 5 China ˆβ 1,j π -0.427-0.926-1.052 (0.194) (0.203) (0.072) R 2 0.369 0.667 0.910 France ˆβ π 1,j -0.245-1.029-1.248 (0.126) (0.174) (0.158) R 2 0.151 0.642 0.795
Regression results: power considerations Our results are based on sample sizes that are short relative to horizon of regressions. We use overlapping changes in the NER t. Use diagnostics suggested by Cochrane (2008) to evaluate whether our correlation findings are spurious. Very unlikely that our results could be generated a RW specification of nominal exchange rates. Similar to literature that argues equity premium is predictable at long-run horizons. Stambaugh (1999) and Boudoukh, Richardson, and Whitelaw (2006) Regressions based on overlapping samples aren t more informative than corresponding short-horizon regressions. Predictability finding is spurious.
Regression results: summary For countries with flexible NER and a Taylor rule The current RER is highly correlated with future changes in the NER at horizons greater than two years. Correlation is stronger the longer is the horizon. The current RER is virtually uncorrelated with future inflation rates at all horizons. For other countries, these results do not hold.
Model We build a model to interpret regression results. Model has two symmetric countries, H and F. We provide intuition using benchmark model: Complete asset markets; Flexible prices; PPP and UIP hold; No internal persistence from consumption habit and interest rate smoothing; No capital.
Preferences of home country E t j=0 [ ] C 1 σ β j t+j 1 σ χ 1 + φ L1+φ t+j + µ (M t+j/p t+j ) 1 σ M, 1 σ M C t : consumption, L t : hours worked, M t : nominal money balances, P t : price level.
Home budget constraint B H,t + NER t B F,t + P t C t + M t Z t = R t 1 B H,t 1 + NER t R t 1B F,t 1 + W t L t + T t + M t 1, Z t : net proceeds from contingent claims, B H,t : nominal bonds from country H, B F,t : nominal bonds from country F, R t : nominal interest rate paid on H bonds, Rt : nominal interest rate paid on F bonds, W t : wage rate, T t : lump-sum profits and taxes.
Complete contingent claims Purchases of claims that payoff in state z t+1, Q H t (z t+1 )X H t (z t+1 ) + NER t Q F t (z t+1 )X F t (z t+1 ) Q H t (z t+1 ) : price of contingent claim that pays 1 unit of HCU in state z t+1, X H t (z t+1 ): quantity of contingent claims in HCU, Q F t (z t+1 ) : price of contingent claim that pays 1 unit of FCU in state z t+1 X F t (z t+1 ) : quantity of contingent claims in FCU. Payoffs from contingent claims X H t 1(z t ) + NER t X F t 1(z t ) Standard result about RER with complete markets: ( ) C σ t = RER t C t
Foreign country Preferences: E t j=0 β j [ (C t+j ) 1 σ 1 σ χ ( M 1 + φ (L t+j) 1+φ t+j /P 1 σm ] t+j) + µ. 1 σ M Budget constraint: NER 1 t B H,t + B F,t + P t C t + M t Z t = NER 1 t R t 1 BH,t 1 + Rt 1B F,t 1 + Wt L t + Tt + Mt 1,
Final goods producers Domestic final goods Y t = Foreign final goods [ ω 1 ρ (X H,t ) ρ + (1 ω) 1 ρ (X F,t ) ρ] 1 ρ [ Yt = ω ( 1 ρ XF,t) ρ + (1 ω) 1 ρ ( ) ] 1 XH,t ρ ρ ω determines home bias in consumption. ρ controls elasticity of substitution between home and foreign goods.
Intermediate goods producers X H,t and X F,t produced from intermediate inputs: X F,t and X H,t ( 1 X H,t = 0 ( 1 X F,t = 0 X H,t (j) ν 1 ν X F,t (j) ν 1 ν ) ν ν 1 dj ) ν ν 1 dj produced from intermediate inputs: ( 1 XF,t = 0 ( 1 XH,t = 0 XF,t (j) ν 1 ν XH,t (j) ν 1 ν ) ν ν 1 dj ) ν ν 1 dj
Intermediate inputs Intermediate inputs produced by monopolists with labor Output from H monopolist X H,t (j) + XH,t (j) = A t L t (j) Output from F monopolist X F,t (j) + XF,t (j) = A t L t (j)
Intermediate inputs Monopolists in home country choose P H,t (j) and P H,t (j) to maximize per-period profits ) ( PH,t (j) (1 + τ X ) W t /A t X H,t (j) ) + (NER t P H,t (j) (1 + τ X ) W t /A t XH,t (j) subject to demand curves of final good producers. Monopolists in foreign country choose P F,t (j) and P F,t (j) to maximize their profits ) ( P F,t (j) (1 + τ X ) Wt /A t XF,t (j) ( + NER 1 t P F,t (j) (1 + τ X ) W t /A t subject to the demand curves of final good producers ) X F,t (j).
Law of one price With flexible prices, law of one price holds. FONCs for monopolists imply: P H,t (j) = NER t P H,t (j) = W t A t NER 1 t P F,t (j) = PF,t (j) = W t A t Monopolists charge gross markup of one due to subsidy that corrects steady-state level of monopoly distortion.
Monetary policy, Taylor rule Home country Foreign country R t R t = (R t 1 ) γ ( ) 1 γ Rπt θπ exp (εr,t ) = ( ) Rt 1 γ ( R(π t ) θπ) 1 γ ( ) exp ε R,t R steady state nominal interest rate; π t P t /P t 1 ; πt Pt /Pt 1; ε R,t and ε R,t are iid policy shocks θ π > 1 so Taylor principle is satisfied.
Technology shock, flex prices, Taylor rule NER denotes $/FCU A t RER t C t and C t * 1.0 0.8 0.6 0.4 0.2 0.0 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 0 10 20 30 40 50 π t and π t * 0 10 20 30 40 50 R t and R t * 0 10 20 30 40 50 NER t 0.00 0.02 0.04 0.06 0.00 0.02 0.04 0.06 0.08 0.10 0.5 0.0 0.5 1.0 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50
Intuition: the role of home bias RER t = C t C t Home bias in consumption has three implications. 1. RER falls (a unit of foregn C basket buys fewer units of home C basket) since home goods are more costly to produce and home consumption basket places a higher weight on these goods. 2. Domestic consumption falls by more than foreign consumption because domestic agents consume more of good whose relative cost of production has risen. 3. Households Euler equations imply that domestic real interest rate must rise by more than foreign real interest rate.
Intuition: the role of the monetary policy rule Taylor rule and Taylor principle imply that high real interest rates are associated with high nominal interest rates and high inflation rates. So R and π rise by more than R and π. π > π Inconsistent with naive intuition that differential inflation rates are key mechanism by which RER returns to its pre-shock level. Relative inflation rates are moving in the wrong direction relative to naive PPP intuition. The only way for RER to revert to its steady state value is via changes in NER (a big depreciation).
Overshooting Since Taylor rule keeps prices relatively stable, fall in RER on impact occurs via an appreciation of home currency. ˆ RER t = κât where Âtis an AR(1). Inter-temporal Euler eq., complete markets, Taylor rule: (Ĉ t Ĉ t ) = ˆR t ˆR t +E t [ (Ĉt+1 Ĉ t+1) (ˆπ t+1 ˆπ t+1 ˆ RER t = θ π (ˆπ t ˆπ t )+E t [ ˆ RER t+1 (ˆπ t+1 ˆπ t+1) ]. Solve forward ˆπ t ˆπ t = ρ A 1 RER ˆ t θ π ρ A where ρ A 1 θ π ρ A < 1. So relative inflation rates move by less than RER. ) ]
Why is there NER overshooting? RER t = NER tp t P t Since RER t falls by more than P t /P t, NER t must initially fall, i.e. the home currency appreciates on impact. Recall that R t rises by more than R. The technology shock is persistent, so there s a persistent gap between R and R. Since UIP holds, domestic currency must depreciate over time to compensate for gap between R and R. In sum, home currency appreciates on impact and then depreciates.
log Regression coefficients ( NERt+j NER t ) = β NER 0,j + β NER 1,j log(rer t ) + ɛ t,t+j. Calculate plim of β 1,j implied by simple model assuming that only technology shocks drive economic fluctuations. Plim β 1,j is negative and grows larger in absolute value with horizon. In model, a low current value of the RER predicts a future depreciation of the domestic currency, so slope of regression is negative. Slope increases with the horizon because cumulative depreciation of home currency increases over time.
Regression coefficients Our model implies plim s of regression coefficients β NER 1,j = 1 ρj A 1 ρ A /θ π, β π 1,j is negative and decreasing in j. High θ π implies small values of β NER 1,j. After a domestic technology shock, π t > π. t. The higher is θ π, the lower is π t and the less the domestic currency needs to depreciate to bring about the required adjustment in the RER. So, the absolute value of β NER 1,j is decreasing in θ π.
Regression coefficients We can also solve for plim of β π 1,j β π 1,j is positive for all j. β π 1,j = 1 ρj A θ π /ρ A 1 Higher is θ π, the lower is β π 1,j for all j ( ) β1,j NER + β1,j RP = 1 ρ j A 1. RER converges to its pre-shock steady state level either through changes in inflation or changes in the NER.
Model-implied NER regression plims Coefficient value 2 1 0 1 2 NER regression (Taylor) Relative price regression (Taylor) 0 10 20 30 40 Horizon (in quarters)
Model-implied NER regression plims Comparing money growth rate and Taylor rules Coefficient value 2 1 0 1 2 NER regression (Taylor) Relative price regression (Taylor) NER regression (money) Relative price regression (money) 0 10 20 30 40 Horizon (in quarters)
Model features Technology shocks, in our benchmark model, can produce negative coefficients in our NER regression that grow with horizon. But, The intuition relies on PPP and UIP. The shocks produce counterfactually large price movements. Develop a richer version of the model that accounts for our exchange rate facts without violating other key features of the data. Incomplete international asset markets. Shocks to the spread between returns on H and F bonds. Nominal rigidities. Capital (see paper, not in slides today).
Deviations from UIP To allow for deviations from UIP, we assume Markets are internationally incomplete; only nominal bonds can be traded across countries. Households derive utility from country H nominal bonds. Easy to generalize this assumption.
Incomplete markets and spread shocks Preferences in country H are E t β j j=0 1+φ t+j C 1 σ t+j 1 σ χl 1 + φ + µ ( Mt P t ) 1 σm 1 σ M +η t V ( BH,t P t ) Spread shock, η t is zero in steady state. Outside of steady state, there may be shocks that put a premium on home (U.S.) bonds, arising from flights to safety or liquidity.
Incomplete markets E t β j j=0 Preferences in country F are (C t+j )1 σ χ(l t+j )1+φ + µ 1 σ 1 + φ ( M t P t ) 1 σm ( B ) H,t +η t V 1 σ M NER t Pt We add a quadratic cost of holding bonds to budget constraints, as in Schmitt-Grohe and Uribe (2003) to prevent unit root in RER.
Incomplete markets With complete markets ( ) C σ t = RER t C t for every state of the world. With incomplete markets, this equation doesn t hold. Instead we impose clearing in the bond market.
Deviations from UIP Ignoring the quadratic costs of bond holdings, household optimality implies E t NER ˆ t+1 = ˆR t ˆR t + η t Consider the classic Fama (1984) regression ˆ NER t+1 = α 0 + α 1 (ˆR t ˆR t ) + ɛ t UIP implies α 0 = 0 and α 1 = 1. In our model, UIP would be rejected because of a negative covariance between ɛ t and (ˆR t ˆR t ). A rise in η t is equivalent to a rise in ε t. Domestic bonds are in zero net supply, yield on domestic bonds must fall leading to a decline in ˆR t ˆR t.
Nominal rigidities We add Calvo-style sticky prices. Local currency pricing and sticky prices break PPP. The effect of technology shocks is little changed. Spread shocks lead to home currency appreciation and have real effects, e.g. decline in consumption.
Medium-scale model We add Interest rate smoothing (γ = 0.75). Habit persistence (Christiano, Eichenbaum, Evans, 2005). Sticky wages (Erceg, Henderson, and Levin, 2000) We parameterize η t to be an AR(1), with autocorrelation 0.85. If exchange rates are a random walk, this is consistent with typical values of ˆR t ˆR t = η t. Also equal to value estimated by Gust et. al. (2016)
Medium-scale model We calibrate σ η, σ A, and ρ A so that we match Persistence and volatility of U.S. per-capita real GDP. Coefficient in the Fama (1984) regression of 0.5. Nothing significant about the nominal rigidities model changes if we insist that the Fama coefficient is 0.0. Can t match a 0.0 regression coefficient in the model without nominal rigidities.
Model-implied regression results With nominal rigidities, our calibration exercise yields ρ A = 0.958 σ A = 0.011 σ η = 0.004 Model-implied probability limit for β 1,j Horizon (in years) 1 3 5 7 10 NER regression -0.446-0.855-1.061-1.199-1.333 Rel.-price reg. 0.074 0.176 0.269 0.340 0.413
Model-implied regression results Without nominal rigidities, our calibration exercise yields ρ A = 0.895 σ A = 0.018 σ η = 0.005 Model-implied probability limit for β 1,j Horizon (in years) 1 3 5 7 10 NER regression -0.414-0.975-1.341-1.581-1.797 Rel.-price reg. 0.184 0.476 0.670 0.797 0.912
Key facts for the model Real and nominal exchange rates commove closely in the short run (Mussa (1986)). RERs are highly inertial (Rogoff (1996)). Real and nominal exchange rates are very volatile.
Exchange Rate Facts Compare model moments to data. ρ RER σ RER Canada 0.986 0.022 (0.872, 0.997) (0.002) With nominal rigidities 0.890 0.023 Without nominal rigidities 0.928 0.024 For some countries, we hit the volatility of the NER and RER fairly well. For a number of countries in our sample, models somewhat understate volatility of NER and RER Example, for Australia, the σ σner = σ RER = 0.040
Exchange Rate Facts Correlation of RER and NER is very high in the data: approximately 0.98 (Mussa, 1986). With nominal rigidities, model generates corr. of 0.96. Without nominal rigidities, model generates corr. of 0.65.
What about capital? Add capital as in CEE Households only own home country capital Results robust
Out of sample forecasting (ongoing work) Our baseline NER regression has correlated errors, even at the 1 quarter horizon. For forecasting, we use ( ) NER i t+j log = β i NERt i 0,j +β1,j i log (RER t )+β2,j i log (RER t 1 ) where i is for each country. Use same time period as our regression results. Training sample of 40 quarters. Use ratio of mean-squared prediction error relative to random walk without drift for forecasting performance.
Out of sample forecasting (ongoing work) RMSPE relative to a random walk: Horizon 1 Month 5 Years Canada 0.95 1.19 Denmark 0.96 0.85 euro area 0.98 1.28 Japan 0.99 1.19 Norway 0.96 0.80 South Korea 0.91 0.56 Sweden 0.95 0.71 Switzerland 0.99 0.74 U.K. 0.98 0.89
Out of sample forecasting (ongoing work) Engel, Mark, West (2007) use panel regressions. We estimate ( ) NER i t+j log = β i NERt i 0,j +β 1,j log (RER t )+β 2,j log (RER t 1 ) Only countries where we have the entire sample period. Training sample of 40 quarters. Use ratio of mean-squared prediction error relative to a random walk without drift for forecasting performance.
Out of sample forecasting (ongoing work) RMSPE relative to a random walk: Horizon 1 Month 5 Years Canada 0.95 0.89 Denmark 0.95 0.79 euro area 0.97 0.84 Japan 0.97 1.09 Norway 0.96 0.76 South Korea 0.95 0.34 Sweden 0.95 0.74 Switzerland 0.99 0.73 U.K. 0.97 0.75 Performance is better with panel structure.
Out of sample forecasting (ongoing work) Extend sample from 1973 through 2016 Add Chile and Mexico. RMSPE relative to a random walk: Horizon 1 Month 5 Years Canada 0.96 0.97 Denmark 0.95 1.22 euro area 0.98 1.28 Japan 0.96 1.01 Norway 0.95 1.10 South Korea 0.93 0.76 Sweden 0.93 1.93 Switzerland 0.97 0.86 U.K. 0.96 1.00 Chile 1.19 1.86 Mexico 0.89 1.14 Substantially worse performance at long horizons.
Model implied RMSPE relative to a random walk
Conclusions RERs are very useful for predicting changes in NERs at medium-to-long horizons. The RER has virtually no forecasting power for future inflation. Home bias and Taylor rules can explain these results. Under a Taylor-rule regime, relative PPP is re-established via changes in the NER, not prices. Medium size DSGE model is consistent with our exchange findings and classic stylized facts about exchange rates emphasized in literature.